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Choice of iterative method for solving nonlinear nonstationary heat conduction problem for a half-space under radiative cooling. (Ukrainian, English) Zbl 1349.74102

Mat. Metody Fiz.-Mekh. Polya 57, No. 4, 179-185 (2014); translation in J. Math. Sci., New York 220, No. 2, 226-234 (2017).
The authors apply the method of reduction to a nonlinear integral Volterra-type equation, the simple iteration method, and the methods of successive approximations and quasilinearization to solve the problem of nonlinear nonstationary radiative interaction of a half-space with a medium. For this class of problems a comparative analysis of efficiency of the approaches is performed. In terms of this analysis, a better convergence of the approach based on the quasilinearization method is found.

MSC:

74F05 Thermal effects in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
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